A three-part tariff refers to a pricing scheme consisting of a fixed fee, a free allowance of units up to which the marginal price is zero, and a positive per-unit price for additional demand beyond that allowance. The three-part tariff and its variations are commonly used in both final-goods and intermediate-goods markets. Recently, the offering of three-part tariffs and the like by dominant firms has become a prominent antitrust issue (e.g., U.S. v. Microsoft Corp. and AMD v. Intel). Existing studies have focused on monopoly models, interpreting the three-part tariff as a price discrimination device. In this paper, I investigate strategic effects of three-part tariffs in a sequential-move game and offer an equilibrium theory of three-part tariffs in a competitive context. I show that, compared with linear pricing equilibrium and two-part tariff equilibrium, a three-part tariff always strictly increases the dominant firm¡¯s (the leader¡¯s) profit when competing against a rival (the follower) with substitute products, in the absence of usual price discrimination motive. To explore the effects of a three-part tariff on welfare, I further perform comparative statics analysis using general differentiated linear demand system. I show that the competitive effect of a three-part tariff in contrast to linear pricing depends on the degree of substitutability between products: Competition is intensified when two products are more differentiated, yet softened when two products are more substitutable. This is in stark contrast with the competitive scenario posed by a two-part tariff: A two-part tariff always enhances competition and gives the highest total surplus of these three pricing schemes. Moreover, the rival firm always gets hurt in both profit and quantity sale when the dominant firm switches from linear pricing to a two-part tariff, yet it enjoys higher profit when the dominant firm moves from a two-part tariff to the more ornate three-part tariff, despite the fact that its quantity and market share are decreased even further. My findings offer a new perspective on three-part tariffs, a perspective which could help antitrust enforcement agencies distinguish the exclusionary three-part tariff from the pro-competitive one.

We extend the traditional literature on bundling and the burgeoning literature on two-sided markets by presenting a theoretical monopoly model of mixed bundling in the context of the portable video game console market¡ªa prototypical two-sided market. We show that the monopoly platform¡¯s dominant strategy is to offer a mixed bundle rather than pure bundle or no bundle. Deviating from both traditional bundling literature and standard two-sided markets literature, we find that, under mixed bundling, both the standalone console price on the consumer side and the royalty rate on the game developer side are lower than their counterparts under independent pricing equilibrium. In our setting, mixed bundling acts as a price discrimination tool segmenting the market more efficiently as well as functions as a coordination device helping solve ¡°the chicken or the egg¡± problem in two-sided markets. After theoretically evaluating the impact mixed bundling has on prices and welfare, we further test the model predictions with new data from the portable video game console market in the early to middle 2000s, during which Nintendo was a monopolist. We employ a reduced form approach, and find empirical support for all theoretical predictions.

Using a game theoretic framework, we show that not only can pay-what-you-want (PWYW) pricing generate positive profits, but it can also be more profitable than charging a fixed price to all consumers. Further, whenever it is more profitable, it is also Pareto-improving. We derive conditions in terms of two cost parameters, namely the marginal cost of production and the psychological cost of the consumer for paying too little compared to her reference price.
The paper makes the
following contributions to the existing literature. First, we endogenize the choice
of pricing strategies—PWYW vs. fixed price. Thus rather than solely focusing
on the profitability of PWYW pricing, we evaluate its profitability vis-a-vis
uniform pricing. To the best of our knowledge this has not been done so far theoretically.
Second, we specify consumer utility to account for both economic and
behavioral considerations. We show that when marginal cost is low and behavioral
considerations are strong, then PWYW pricing can exploit the deadweight
loss present under the uniform price to gain additional profit at the cost of serving
some free riders. Therefore, PWYW pricing can be more profitable than charging
a fixed price especially when the marginal cost is low and the deadweight loss is
high. Third, we demonstrate PWYW pricing is more attractive when the cost of price setting is considerable or the market size is small.

We consider second-degree price discrimination for two types of consumers. When the net-of-cost valuation functions cross at least once at some positive quantity, it is always optimal to serve both types of consumers. Moreover, the type with the higher valuation peak always gets the socially efficient quantity. The sufficient and necessary condition for the overall efficiency is the peak of each type's net-of-cost valuation is above the other type's net-of-cost valuation at that peak quantity. For two general linear demands, we quantify the degree of efficiency, upward and downward distortions.

This paper is motivated by an institutional detail of stock market trading: tick size constraint, which requires quotes to be on a discrete pricing grid. Our findings suggest that this discrete pricing leads to two-sided pricing; whereas continuous pricing results in only one-sided pricing. Such discreteness gives rise to endogenous vertical differentiation among platforms, which can explain market fragmentation in the US stock exchange industry.

We present an exclusionary theory of all-units discounts schemes. These schemes offer a per-unit discount to all units purchased if the customer's purchase reaches a pre-specified quantity threshold. We demonstrate that when a dominant firm competes with a capacity-constrained rival, it is possible for the dominant firm to use all-units discounts to leverage its market power in the non-contestable portion to influence the contestable portion of the demand in single-product markets and to partially foreclose the small rival. Our theory suggests that pricing below cost is not necessary for all-units discounts schemes to be exclusionary and that a standard price-cost test may not be useful in assessing the exclusionary effects of all-units discounts. We advocate a rule of reason approach based on a comprehensive analysis of market structure, the nature of discount programs, exclusionary effects, efficiency, and the welfare consequences of these practices.

All-units discounts (AUD) are pricing schemes that lower a buyer’s marginal price on every unit purchased when the buyer’s purchase exceeds or is equal to a pre-specified threshold. The AUD and related conditional rebates are commonly used in both final-goods and intermediate-goods markets. Although the existing literature has thus far focused on interpreting the AUD as a price discrimination tool, investment incentive program, or rent-shifting instrument, the antitrust concerns on the AUD and related conditional rebates are often their plausible exclusionary effects.
In this article, we investigate strategic effects of volume-threshold based AUD used by a dominant firm in the presence of a capacity-constrained rival. We find that the AUD always increase the dominant firm’s profits, sales volume and market share over linear pricing or two-part tariff. At the same time, the AUD adopted by a dominant firm lead to “partial foreclosure” of an equally or more efficient rival, in the sense that the rival’s profit, sales volume and market share are strictly reduced, as compared to linear pricing. The buyer’s surplus and total surplus could be either lower or higher under AUD, depending on the rival's capacity level relative to the demand size. The intuition for our findings is that, due to the limited capacity of the rival, the dominant firm, that has a “captive” portion of the buyer’s demand in the context of a single product, is able to use the AUD to leverage its market power on the “captive” to “competitive” portion of the demand, much like the tied-in selling strategy in the context of multiple products. Our analysis applies to other similar settings in which the dominant firm has some “captive” market when it offers “must-carry” brands or a wider range of products.

We propose a theoretical model to explain two salient features of the U.S. stock exchange industry: (i) sizable dispersion and frequent changes in stock exchange fees; and (ii) the proliferation of stock exchanges offering identical transaction services, highlighting the role of discrete pricing. Exchange operators in the United States compete for order flow by setting “make” fees for limit orders (“makers”) and “take” fees for market orders (“takers”). When traders can quote continuous prices, the manner in which operators divide the total fee between makers and takers is irrelevant because traders can choose prices that perfectly counteract any fee division. If such is the case, order flow consolidates on the exchange with the lowest total fee. The one-cent minimum tick size imposed by the U.S. Securities and Exchange Commission’s Rule 612(c) of Regulation National Market Systems for traders prevents perfect neutralization and eliminates mutually agreeable trades at price levels within a tick. These frictions (i) create both scope and incentive for an operator to establish multiple exchanges that differ in fee structure in order to engage in second-degree price discrimination; and (ii) lead to mixed-strategy equilibria with positive profits for competing operators, rather than to zero-fee, zero-profit Bertrand equilibrium. Policy proposals that require exchanges to charge one side only or to divide the total fee equally between the two sides would lead to zero make and take fees, but the welfare effects of these two proposals are mixed under tick size constraints.

This paper studies probabilistic selling with vertically differentiated products when firms compete and consumers anticipate the potential post-purchase regret raised by possibly obtaining inferior products. Intuitively, anticipated regret hurts the attractiveness of probabilistic selling. However, we find that probabilistic selling can be more profitable for the random product provider, and more likely to arise with anticipated regret than without it. This is due to ¡°reverse quality discrimination¡± (perceived quality of the random product is decreasing in consumers¡¯ tastes for quality at the competition margin) in the presence of anticipated regret, which increases the perceived differentiation, and where the random product may still maintain sufficient attractiveness for infra-marginal consumers. Moreover, the anticipated regret may hurt its competitor¡¯s profit.

We consider second-degree price discrimination with and without single-crossing condition. The comparison with uniform pricing shows that, for two linear demands, second-degree price discrimination can not only result in a market foreclosure (both markets are served under uniform pricing while one of them is not served under second-degree price discrimination), but also such foreclosure can increase total profit, total output and total surplus. The total surplus could be higher with the market foreclosure and also lower without the foreclosure,.

This paper investigates the viability of Pay-What-You-Want (PWYW) pricing when firms compete without restrictions of a minimum payment requirement or of consumer knowledge about firms' costs. We show that the equilibrium outcomes are different when underpayers, consumers who pay less than marginal cost, are present as opposed to when they are absent. In particular, when PWYW pricing is practiced without restricting the presence of underpayers and without any minimum payment requirement, then the only two equilibrium structures are: either both firms use the posted price and earn zero profits, or one firm adopts PWYW pricing and the other uses the posted price. The asymmetric pricing equilibrium leads to a softening of price competition where both firms earn positive profits and the Bertrand Trap is broken.